Waveguide mach-zehnder optical isolator utilizing transverse magneto-optical phase shift

ABSTRACT

A device and method for optical isolation for use in optical systems is disclosed. The device provides for a waveguide optical isolator fabricated using two arms, made of optical waveguides comprising magneto-optical material, in a Mach-Zehnder interferometer configuration. The device of the present invention operates using the TM mode of a light wave and, thus, does not require phase-matching of TM and TE modes. Further, the present invention does not use polarizers to extinguish the optical feedback.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0001] The invention described herein was funded in part by a grant fromAFOSR/DARPA Program, Contract No. F49620-99-1-0038, and in part by DARPAFAME Program, Contract No. N0017398-1-G014. The United States Governmentmay have certain rights under the invention.

FIELD OF THE INVENTION

[0002] The present invention relates generally to optical communicationsystems. In particular, the present invention relates to waveguideoptical isolators.

BACKGROUND OF THE INVENTION

[0003] Optical isolators are essential elements in many optical systemsfor protecting a light source, such as a laser, from being exposed tolight which is reflected back at the light source. Such reflected light,known as “optical feedback,” may cause the light source to becomeunstable or may even damage the light source. The problem is especiallydifficult in optical systems employing lasers that emit a relativelyhigh output beam power where even surfaces of transmissive opticalelements, or relatively small discontinuities or mismatches in opticalwaveguides can produce sufficient reflections to give rise todeleterious optical feedback.

[0004] It is known to incorporate an optical isolator in the path of thelaser output beam, near the laser cavity exit aperture, to isolate thelaser from reflected laser light and thereby avoid or reduce opticalfeedback. An optical isolator permits the forward transmission of aradiation beam, in this case the laser output beam, while simultaneouslypreventing the reverse transmission of the same radiation beam, with ahigh degree of extinction. Thus, the laser energy reflected back towardsthe laser from various sources of reflection is trapped, extinguished orreflected by the optical isolator.

[0005] Optical isolators based on the Faraday polarization rotationeffect are available for use in laser systems. Such a conventionaloptical isolator is illustrated in FIG. 1. The conventional opticalisolator 50 includes, a first polarizer 58 for linearly polarizing alight wave in a first direction 62 and a second polarizer 60 forlinearly polarizing a light wave in a second direction 64, alongitudinal magnet 52 surrounding a magneto-optical medium 54, whichmay be in the form of an optical waveguide, for example. The magnet 52applies a longitudinal magnetic field 56 to the magneto-optical medium54.

[0006] In operation, an incident light wave is polarized by firstpolarizer 58 in a first direction 62. If the incident light wave isplane polarized, the first direction 62 of polarization should coincidewith the polarization of the incident light wave as it leaves the lightsource. This polarized light wave then enters the magneto-optical medium54, where a permanent magnet 52, or alternatively an electromagnet,applies a magnetic field 56 that causes a rotation of the plane ofpolarization of the light wave by 45 degrees, as shown by directionalarrows 70, to align the direction of polarization of the light wave withthe second polarizer 60 having a direction 64 of polarization set at 45degrees from that of the first linear polarizer 58. In this way, aforward propagating light wave passes through the conventional opticalisolator 50 with little attenuation.

[0007] A light wave of unknown polarization 74 propagating in thebackward direction is first linearly polarized by the second polarizer60. Since the polarization of light waves traveling in the backwarddirection is unknown, only light waves traveling in the backwarddirection with the polarization direction 64 of the second polarizer 60will pass second polarizer 60 and enter the magneto-optical medium 54.Once propagating in the magneto-optical material 54, the polarization ofthe backward propagating light wave is rotated by 45 degrees, in thesame sense as the rotation of the forward propagating light wave,causing the direction of polarization of the backward propagating lightwave exiting the magneto-optical medium 54 to be polarized at 90 degreeswith respect to the direction of the first polarizer 58. Therefore, thebackward propagated light wave will not pass the first polarizer 58.

[0008] With such a conventional optical isolator 50, however, there hasbeen the problem of the need for a bulky magnet for applying alongitudinal magnetic field, stringent modal phase-matching for the TMand TE modes of light waves propagating in the magneto-optical mediumand addition of auxiliary components such as polarizers 58, 60. Further,non-uniformities in the longitudinal magnetic field introducenon-uniform polarization rotation across a light wave passing throughthe magneto-optical medium 54. Unless the light wave dimension is madeequal to or smaller than the cross-section of uniform Faraday rotation,these non-uniformities limit the extinction ratio obtainable by theconventional optical isolator.

[0009] There exists a need for an optical isolator which eliminates theneed for a bulky magnet for applying a longitudinal magnetic field,modal phase-matching and the need for polarizers.

SUMMARY OF THE INVENTION

[0010] In accordance with the present invention, there is provided awaveguide optical isolator having first and second optical waveguidearms formed at least in part with a material that exhibits a transversemagneto-optic non-reciprocal phase shift effect, the two opticalwaveguide arms being arranged in a Mach-Zehnder interferometerconfiguration. Transverse magnetic fields of equal magnitude arerespectively applied to the two magnetically active optical waveguidearms of the Mach-Zehnder interferometer in opposite transversedirections to cause non-reciprocal phase shifts of equal magnitude butof opposite signs for light waves propagating in the two magneticallyactive optical waveguide arms. Further, by adjusting the path lengths ofthe two optical waveguide arms, a 90 degree reciprocal phase shift of alight wave propagating in the first optical waveguide arm with respectto a light wave propagating in the second optical waveguide arm of thedevice is achieved. During forward propagation of a light wave in thefirst magnetically active optical waveguide arm, the 90 degreereciprocal phase shift is combined with a −45 degree forward propagationnon-reciprocal phase shift so as to provide a net phase shift of +45degrees for the light wave after propagation through the firstmagnetically active optical waveguide arm. Forward propagation of alight wave through the second magnetically active optical waveguide armresults in a +45 degree forward propagation non-reciprocal phase shift.Accordingly, when light waves that were initially in phase havepropagated in the forward direction through the first and secondmagnetically active optical waveguide arms are combined, the two lightwaves which are remain in phase interfere constructively. For backwardpropagation of a light wave through the first magnetically activeoptical waveguide arm, the light wave undergoes a 90 degree reciprocalphase shift combined with a +45 degree backward propagationnon-reciprocal phase shift to cause a net phase shift of 135 degrees ofthe light wave after propagating through the first magnetically activeoptical waveguide arm. A light wave after propagating through the secondmagnetically active optical waveguide arm is phase shifted by −45 degreebackward propagation non-reciprocal phase shift. Accordingly, when twolight waves, which were initially in phase propagating through the firstand second magnetically active optical waveguide arms, respectively, arecombined, they are 180 degrees out of phase and interfere destructively.In this manner, a light wave propagating in the forward directionthrough the waveguide optical isolator of the present invention, whichis approximately equally divided for propagation in the first and secondoptical waveguide arms and then recombined, will pass through the devicewith relatively low attenuation, while a light wave propagating in thereverse direction in the waveguide optical isolator, which isapproximately equally divided for propagation in the first and secondoptical waveguide arms and then recombined, is extinguished bydestructive interference in the Mach-Zehnder interferometer.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] For a complete understanding of the present invention and theadvantages thereof, reference is now made to the following descriptiontaken in conjunction with the accompanying drawings in which likereference numbers indicate like features, components and method steps,and wherein:

[0012]FIG. 1 is an illustration of a conventional optical isolator basedon the Faraday polarization rotation effect;

[0013]FIG. 2 is an illustration of a waveguide optical isolatorfabricated in a Mach-Zehnder interferometer configuration in accordancean exemplary embodiment of the present invention;

[0014]FIG. 3 is an illustration of the structure of a magneticallyactive optical waveguide in accordance with an exemplary embodiment ofthe present invention; and

[0015]FIG. 4 is an illustration of a test apparatus for testingwaveguide optical isolators fabricated in the Mach-Zehnderinterferometer configuration of FIG. 2 in accordance with an exemplaryembodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0016] Now referring to the drawing, FIG. 2 illustrates a waveguideoptical isolator 100 fabricated in a Mach-Zehnder interferometerconfiguration in accordance with an exemplary embodiment of the presentinvention. The waveguide optical isolator 100 includes an input opticalwaveguide section 102, an input optical waveguide Y-branch 132, twooptical waveguide arms 104, 106, an output optical waveguide Y-branch130 and an output optical waveguide section 108. The input opticalwaveguide Y-branch 132 approximately equally divides a light wavepropagating in the forward direction in the input optical waveguidesection 102 into two divided light waves and provides a respective oneof the two divided light waves to each of the optical waveguide arms104, 106 without changing the mode of propagation. The input opticalwaveguide Y-branch 132 also combines respective light waves propagatingin the backward direction in the two optical waveguide arms 104, 106 andprovides the combined light wave to the input waveguide section 102without changing the mode of propagation. The output optical waveguideY-branch 130 combines respective light waves propagating in the forwarddirection and provides the combined light wave to the output opticalwaveguide section 108 without changing the mode of propagation. Theoutput optical waveguide Y-branch 130 also approximately equally dividesa light wave propagating in the backward direction in the output opticalwaveguide section 108 into two divided light waves and provides each ofthe two divided light waves to respective ones of the two opticalwaveguide arms 104, 106 without changing the mode of propagation.

[0017] Referring to FIG. 3, in an exemplary embodiment, the waveguide isfabricated by growing a bismuth-, lutetium-, neodymium-iron garnet film240 (Bi,Lu,Nd)₃(Fe,Al) ₄O₁₂ by liquid phase epitaxyo on a [111] orientedgallium gadolinium garnet (GGG) substrate. The bismuth-, lutetium-,neodymium-iron garnet film 240 is a magnetically active material whichcan cause non-reciprocal, controllable phase shift of a light wavepropagating through it based upon a transverse magnetic field appliedthereto. Alternatively, this film 240 could be bismuth-, lutetium-irongarnet or yttrium iron garnet (YIG), rare-earth substituted yttrium-irongarnet or rare-earth substituted iron garnet. Using a bismuth-,lutetium-, neodymium-iron garnet film 240, the film-substrate latticemismatch is 0.001 nm, causing minimum stress-induced anisotropy. Thefilm 240 has in-plane magnetization, and a refractive index of 2.2403for the TM mode at λ=1.55 μm. The film 240 initially has a thickness ofapproximately 1.65 μm.

[0018] Before the rib waveguides are patterned, the films 240 arethinned to optimize the non-reciprocal response to a thickness rangingfrom 0.3 μm to 1.0 μm; in an exemplary embodiment this optimum thicknessis approximately 0.5 μm. Since thickness tuning improves the phase shiftper length, proper tuning yields a shorter device and hence reduces thetotal absorption loss in the waveguide optical isolator 100. Straightridge waveguides are then patterned on the film 240 by conventionalphotolithographic and etching techniques. As illustrated in FIG. 3, theridge waveguides have a width ranging from 0.5 μm to 6.0 μm, in anexemplary embodiment this optimum width is approximately 2.0 μm; a 0.5μm waveguide height; and a 0.07 μm rib height and are fabricated byphotoresist patterning and phosphoric-acid wet etching. In thisexemplary embodiment the etch rate is 0.01 μm/min at 57 degrees Celsius.

[0019] A waveguide optical isolator 100 is then patterned onto a singlechip by a photolithographic direct laser writing system. The resistpatterns are made by focusing an Argon (Ar) laser beam (λ=360 nm)directly onto a photoresist-coated sample with computer-controlled XYZtranslation stages and shutter. In an exemplary embodiment the totallength of the fabricated waveguide optical isolator 100 is 8.0 mm, whichincludes 3.3 mm long optical waveguide arms, 0.4 mm long output andinput waveguide Y-branches 130, 132, and 3.9 mm long input and outputwaveguide sections 102, 108. The separation between the opticalwaveguide arms 104, 106 is 24.4 μm, where the output and input waveguideY-branches 130, 132 are each formed at a non critical angular separationof the branches ranging from 0.1 to 3 degrees.

[0020] The reciprocal phase shift is obtained by forming the opticalwaveguide arms 104, 106 with a difference in length, herein referred toas “path length.” The path length has a direct impact on the reciprocalphase shift of each light wave 112, 114 after propagating throughrespective optical waveguide arms 104, 106. In this exemplary embodimentthe top optical waveguide arm 104 has a shorter path length than thebottom optical waveguide arm 106. The path lengths are selected suchthat a light wave 114, originating from the input waveguide Y-branch 132propagates in a forward direction through the bottom optical waveguidearm 106 to reach output waveguide Y-branch 130 with a phase differenceof +90 degrees with respect to a light wave 112 also originating frominput waveguide Y-branch 132 propagating in a forward direction throughthe top optical waveguide arm 104 and reaching output waveguide Y-branch130. Further, a light wave 114, originating from the output waveguideY-branch 130 propagates in a backward direction through the bottomoptical waveguide arm 106 to reach the input waveguide Y-branch 132having a phase difference of 90 degrees with respect to a light wave 112also originating from the output waveguide Y-branch 130 and propagatingin the backward direction through the top optical waveguide arm 104 toreach the input waveguide Y-branch 132. This reciprocal phase shift isthe result of the different path lengths of the two optical waveguidearms 104, 106. In the exemplary embodiment of the present inventiondescribed above with reference to FIG. 3, the top optical waveguide arm104 is a quarter wavelength ±30%, which is 0.2 μm, shorter than thebottom optical waveguide arm 106 in order to achieve the reciprocalphase shifts described above. This 0.2 μm total path length differenceproduces less than 0.006 degrees of additional non-reciprocal phaseshift, and thus the unequal optical waveguide arm lengths do nototherwise affect the operation of the device.

[0021] As described above the waveguides contain magneto-opticalmaterial in the waveguides of the optical waveguide arms 104, 106, whichprovide non-reciprocal phase shifts when a transverse magnetic field isapplied to each optical waveguide arm 104, 106. The amount ofnon-reciprocal phase shift depends upon the path lengths of each opticalwaveguide arm 104, 106, and the magnitude and direction of thetransverse magnetic field applied thereto. As described above, in thisexemplary embodiment the top optical waveguide arm 104 is 3.3 mm minus0.2 μm and the bottom optical waveguide arm 106 is 3.3 mm. As shown inFIG. 2, each of the top and bottom magnetically active optical waveguidearms 104, 106 have a respective transverse magnetic fields appliedthereto. The respective transverse magnetic fields are of the samemagnitude but are opposite in direction. The magnitude and transversedirection of the magnetic fields are arranged so as to produce anon-reciprocal 45 degree phase shift of a light wave propagating throughthe top optical waveguide arm 104 in a forward direction, anon-reciprocal −45 degree phase shift of a light wave propagatingthrough the bottom optical waveguide arm 106 in a forward direction, anon-reciprocal −45 degree phase shift of a light wave propagatingthrough the top optical waveguide arm 104 in a backward direction, and anon-reciprocal 45 degree phase shift of a light wave propagating throughthe bottom optical waveguide arm 106 in a backward direction. Thus, asillustrated on FIG. 2, the end result is constructive interference atthe output waveguide Y-branch 130 of light waves propagated in theforward direction in the top and bottom optical waveguide arms 104, 106,and +180 out of phase destructive interference at the input waveguideY-branch 132 of light waves propagated in the backward direction in thetop and bottom optical waveguide arms 104, 106. This allows a forwardpropagating light wave to pass through the optical isolator 100 whileextinguishing a backward propagating light wave.

[0022]FIG. 4 illustrates a waveguide optical isolator testing apparatusto test a sample waveguide optical isolator 100 of the presentinvention. Testing apparatus 300 includes a laser source 302, e.g. laserdiode, an optical fiber half-wave plate and an optical fiberquarter-wave plate 304, optical isolator 100, a camera 320, monitor 318,and a photodetector 322.

[0023] The waveguide optical isolator 100 is tested using testingapparatus 300 by end fire coupling a light wave from the laser source302 to an optic fiber 324, connected to an optical fiber half-wave plateand an optical fiber quarter-wave plate 304, focusing the light from theoptical fiber half-wave plate and quarter-wave plate so as to cause thepropagation of TM mode light waves in the ridge waveguides of theoptical waveguide isolator 100, and monitoring the light wave from theoutput waveguide section 108 with a silicon photodiode 322, a camera 320and monitor 318. An output spatial filtering comprises a lens 326 and anaperture 328 is used to couple light only from the waveguide opticalisolator 100 and, therefore, to eliminate any extraneous light beforephotodetection.

[0024] Isolation measurements are made after applying opposing magneticfields to the optical waveguide arms 104, 106, of the waveguide opticalisolator 100, thus yielding an opposite sense of non-reciprocal phaseretardation shift between optical waveguide arms 104, 106 in accordancewith the non-reciprocal phase shift requirements described above. Thisis done by placing electromagnets on opposite sides of the waveguideoptical isolator 100 with a separation of 6 mm. The electromagnets aremounted on XYZ translation stages for fine spatial adjustment of themagnetic field as applied to the first and second magnetically activeoptical waveguide arms 104, 106. Further, the backward propagation for alight wave is simulated by reversing the polarities for bothelectromagnets, and the ratio in output light intensities for the twopolarities of magnetic fields is taken as the isolation ratio.

[0025] Measured extinction ratios of 19 dB with 2 dB excess loss at awavelength of λ1.54 μm were obtained, where excess loss is defined asany loss other than material absorption, input mode coupling andwaveguide Y-branch loss. In addition, the above extinction ratio andexcess losses have been observed for wavelengths ranging from λ=1.4 μmto λ=1.7 μm.

[0026] The present invention provides for a waveguide optical isolatorfabricated using two arms, made of optical waveguides comprisingmagneto-optical material, in a Mach-Zehnder interferometerconfiguration. Because the waveguides of the device operate in the TMmode of propagation, there is no need to phase match TM and TE modes. Itis noted that operation of the waveguides in the TE mode, is alsopossible by introducing horizontal asymmetries in the ridge waveguides.Furthermore, other optical waveguide configurations may be used insteadof the ridge waveguide.

[0027] Although the present invention has been described in detail withreference to specific exemplary embodiments thereof, variousmodifications, alterations and adaptations may be made by those skilledin the art without departing from the spirit and scope of the invention.In particular, the above described invention can be implemented withmaterials that exhibit the transverse magneto-optic non-reciprocal phaseshift effect other than BiLuNe—IG or YIG. It is intended that theinvention be limited only by the appended claims.

1. A waveguide optical isolator for providing low attenuation for alight propagating in a forward direction and high attenuation for alight propagating in a backward direction, said optical systemcomprising: an input optical waveguide section; a first and secondoptical waveguide arms coupled to said input optical waveguide sectionfor each receiving approximately an equal portion of an input light wavepropagating in a forward direction and respectively propagating eachapproximately equal portion as first and second light waves in theforward direction in said first and second optical waveguide arms, andfor providing to said input optical waveguide section a combined firstand a second light wave propagating in a backward direction from saidfirst and second optical waveguide arms, respectively, said first andsecond optical waveguide arms being fabricated at least in part with amaterial that provides a transverse magneto-optical non-reciprocal phaseshift, said first optical waveguide arm being longer than the secondoptical waveguide arm by a length that results in a 90 degree reciprocalphase difference of said first light wave propagating through said firstoptical waveguide arm relative to said second light wave propagatingthrough said second optical waveguide arm; first and second magnetsapplying respective transverse magnetic fields to said first and secondoptical waveguide arms, said transverse magnetic fields being of thesame magnitude but of opposite polarity so as to cause a non-reciprocal+45 degree phase shift for said first light wave propagating in theforward direction in said first optical waveguide arm and a −45 degreenon-reciprocal phase shift for said second light wave propagating in theforward direction in said second optical waveguide arm, said magneticfields causing a non-reciprocal −45 degree phase shift for said firstlight wave propagating in the backward direction in said first opticalwaveguide arm and a +45 degree nonreciprocal phase shift for said secondlight wave propagating in the backward direction in said second opticalwaveguide arm; and an output optical waveguide section coupled to saidfirst and second optical waveguide arms for receiving in combinationsaid first and second light waves propagating in a forward directionfrom said first and second optical waveguide arms, and for providingapproximately an equal portion of a feedback light wave propagating inthe backward direction in the output optical waveguide section to eachof said first and second optical waveguide arms for respectivelypropagating therein as said first and second light waves.
 2. Thewaveguide optical isolator of claim 1, wherein said input opticalwaveguide section is coupled to said first and second optical waveguidearms through a first optical waveguide Y-branch having a first branchcoupled to the input optical waveguide section and second and thirdbranches coupled to the first and second optical waveguide arms,respectively.
 3. The waveguide optical isolator of claim 2, wherein thesecond and third branches of the first optical waveguide Y-branch havean angular separation in the range of 0.1 to 3 degrees.
 4. The waveguideoptical isolator of claim 1, wherein said output optical waveguidesection is coupled to said first and second optical waveguide armsthrough a second optical waveguide Y-branch having a first branchcoupled to the output optical waveguide section, and second and thirdbranches coupled to the first and second optical waveguide arms,respectively.
 5. The waveguide optical isolator of claim 4, wherein thesecond and third branches of the second optical waveguide Y-branch havean angular separation in the range of 0.1 to 3 degrees.
 6. The waveguideoptical isolator of claim 1, wherein said material providing saidtransverse magneto-optical non-reciprocal phase shift is bismuth-,lutetium-, neodymium-iron garnet.
 7. The waveguide optical isolator ofclaim 1, wherein said material providing said transverse magneto-opticalnon-reciprocal phase shift is bismuth-, lutetium-iron garnet.
 8. Thewaveguide optical isolator of claim 1, wherein said material providingsaid transverse magneto-optical non-reciprocal phase shift isyttrium-iron garnet.
 9. The waveguide optical isolator of claim 1,wherein said material providing said transverse magneto-opticalnon-reciprocal phase shift is rare-earth substituted yttrium-irongarnet.
 10. The waveguide optical isolator of claim 1, wherein saidmaterial providing said transverse magneto-optical non-reciprocal phaseshift is rare-earth substituted iron garnet.
 11. The waveguide opticalisolator of claim 6, wherein said material providing said transversemagneto-optical non-reciprocal phase shift is in the range of 0.3 μm to1.0 μm thick.
 12. The waveguide optical isolator of claim 1, whereinsaid first and second magnets are permanent magnets, said first magnetapplying a transverse magnet field to said first optical waveguide armin a first transverse direction and said second magnet applying atransverse magnet field to said second optical waveguide arm in a secondtransverse direction.
 13. The waveguide optical isolator of claim 1,wherein said first and second magnets are electromagnets, said firstmagnet applying a transverse magnet field to said first opticalwaveguide arm in a first transverse direction and said second magnetapplying a transverse magnet field to said second optical waveguide armin a second transverse direction.
 14. The waveguide optical isolator ofclaim 6, wherein said input optical waveguide section, first and secondoptical waveguide arms and said output optical waveguide section are ribwaveguides having a width ranging from 0.5 μm to 6.0 μm.
 15. Thewaveguide optical isolator of claim 6, wherein said input opticalwaveguide section, first and second optical waveguide arms and saidoutput optical waveguide section are rib waveguides having a waveguideheight of 0.5 μm.
 16. The waveguide optical isolator of claim 6, whereinsaid input optical waveguide section, first and second optical waveguidearms and said output optical waveguide section are rib waveguides havinga rib height of 0.07 μm.
 17. The waveguide optical isolator of claim 6,wherein said input optical waveguide section is 3.9 mm long.
 18. Thewaveguide optical isolator of claim 6, wherein said output waveguidesection is 3.9 mm long.
 19. The waveguide optical isolator of claim 2,wherein said first optical waveguide Y-branch is 0.4 mm long.
 20. Thewaveguide optical isolator of claim 4, wherein said second opticalwaveguide Y-branch is 0.4 mm long.
 21. The waveguide optical isolator ofclaim 1, wherein said first optical waveguide arm is spaced 24.4 μm fromsaid second optical waveguide arm.
 22. The waveguide optical isolator ofclaim 1, wherein said first magnet is spaced 6 mm from said secondmagnet.
 23. The waveguide optical isolator of claim 6, wherein saidfirst and second light waves each have a wavelength in vacuum of 1.55 μmand said first optical waveguide arm is 0.2 μm shorter than said secondoptical waveguide arm.
 24. The waveguide optical isolator of claim 6,wherein said first optical waveguide arm is approximately a quarterwavelength of said first and second light waves in said first and secondoptical waveguide arms shorter than said second optical waveguide arm.25. The waveguide optical isolator of claim 6, wherein said waveguideoptical isolator is operable in the wavelength range from 1.4 μm to 1.7μm.
 26. A method of isolating a light source from optical feedbackcomprising: providing an input light wave from said light source to aninput optical waveguide section; providing said input light wave fromsaid input optical waveguide section to a first and second opticalwaveguide arms coupled to said input optical waveguide section, saidinput optical waveguide section being coupled to provide approximatelyan equal portion of said input light wave propagating in a forwarddirection to each of said first and second optical waveguide arms forrespective propagation therein as a first and second light wave in aforward direction and to provide said input optical waveguide section acombined first and second light wave propagating in a backward directionfrom said first and second optical waveguide arms, respectively, saidfirst and second optical waveguide arms being fabricated at least inpart with a material that provides a transverse magneto-opticalnon-reciprocal phase shift, said first optical waveguide arm beinglonger than said second optical waveguide arm by a length that resultsin a 90 degree reciprocal phase difference of said first light wavepropagating through said first optical waveguide arm relative to saidsecond light wave propagating through said second optical waveguide arm;applying first and second transverse magnetic fields to said first andsecond optical waveguide arms, respectively, so as to cause anon-reciprocal +45 degree phase shift for said first light wavepropagating in the forward direction in said first optical waveguide armand a −45 degree non-reciprocal phase shift for said second light wavepropagating in the forward direction in said second optical waveguidearm, said magnetic fields causing a non-reciprocal −45 degree phaseshift for said first light wave propagating in the backward direction insaid first optical waveguide arm and a +45 degree non-reciprocal phaseshift for said second light wave propagating in the backward directionin said second optical waveguide arm; and receiving in combination saidfirst and second light waves propagating in said forward direction fromsaid first and second optical waveguide arms, respectively, at an outputoptical waveguide section coupled said first and second opticalwaveguide arms, and for providing approximately an equal portion of afeedback light wave propagating in the backward direction in said outputoptical waveguide section to each of said first and second opticalwaveguide arms for backward propagation therein as said first and secondlight waves.
 27. The method of claim 26, wherein said input light waveis provided to said first and second optical waveguide arms through afirst optical waveguide Y-branch coupling said input waveguide sectionto said first and second optical waveguide arms.
 28. The method of claim27, wherein said first optical waveguide Y-branch has a first branchcoupled to said input optical waveguide section, and second and thirdbranches coupled to said first and second optical waveguide arms,respectively, said second and third branches having an angularseparation in the range of 0.1 to 3 degrees.
 29. The method of claim 26,wherein said output optical waveguide section receives said first andsecond light waves through a second optical waveguide Y-branch couplingsaid output optical waveguide section to said first and second opticalwaveguide arms.
 30. The method of claim 29, wherein said second opticalwaveguide Y-branch has a first branch coupled to said output opticalwaveguide section, and second and third branches coupled to said firstand second optical waveguide arms, respectively, said second and thirdbranches having an angular separation in the range of 0.1 to 3 degrees.31. The method of claim 26, wherein said material providing saidtransverse magneto-optical non-reciprocal phase shift comprisesbismuth-, lutetium-neodymium-iron garnet.
 32. The method of claim 26,wherein said material providing said transverse magneto-opticalnon-reciprocal phase shift comprises bismuth-lutetium-iron garnet. 33.The method of claim 26, wherein said material providing said transversemagneto-optical non-reciprocal phase shift comprises yttrium irongarnet.
 34. The method of claim 26, wherein said material providing saidtransverse magneto-optical non-reciprocal phase shift comprisesrare-earth substituted yttrium-iron garnet.
 35. The method of claim 26,wherein said material providing said transverse magneto-opticalnon-reciprocal phase shift comprises rare-earth substituted iron garnet.36. The method of claim 31, wherein said material providing saidtransverse magneto-optical non-reciprocal phase shift has a thicknessranging from 0.3 μm to 1.0 μm.
 37. The method of claim 31, wherein saidinput optical waveguide section, first and second optical waveguide armsand said output optical waveguide section each has a width ranging from0.5 μm to 6.0 μm.
 38. The method of claim 31, wherein said input opticalwaveguide section, first and second optical waveguide arms and saidoutput optical waveguide section each has a waveguide height of 0.5 μm.39. The method of claim 31, wherein said input optical waveguidesection, first and second optical waveguide arms and said output opticalwaveguide section are rib waveguides having a rib height of 0.07 μm. 40.The method of claim 26, wherein said input optical waveguide section hasa length of 3.9 mm.
 41. The method of claim 26, wherein said outputoptical waveguide section has a length of 3.9 mm.
 42. The method ofclaim 27, wherein said first optical waveguide Y-branch has a length of0.4 mm.
 43. The method of claim 29, wherein said second opticalwaveguide Y-branch has a length of 0.4 mm.
 44. The method of claim 26,wherein said first optical waveguide arm is spaced from said secondoptical waveguide arm by 24.4 μm.
 45. The method of claim 31, whereinsaid first and second transverse magnetic fields are respectivelyapplied by first and second magnets spaced from one another by 6 mm. 46.The method of claim 31, wherein said first and second light waves eachhave a wavelength in vacuum of 1.55 μm and said first optical waveguidearm is 0.2 μm longer than said second optical waveguide arm.
 47. Themethod of claim 26, wherein said first optical waveguide arm isapproximately a quarter wavelength of said first and second light wavespropagating in said first and second optical waveguide arms shorter thansaid second optical waveguide arm.
 48. The method of claim 31 furthercomprising said input optical waveguide section, said first and secondoptical waveguide arms and said output optical waveguide section areeach rib waveguides having a width of 2.0 μm, a height of 0.5 μm and arib height of 0.07 μm, wherein effective optical isolation is providedfor wavelengths in the range 1.4 μm to 1.7 μm.